1.
BAUMOL MODEL:
INVENTORY DEMAND FOR
MONEY
Prof. Prabha Panth,
Osmania University,
Hyderabad

2.
Demand for Money
 Keynes assumed Transaction and
Precautionary DM = f(Y), so changes in interest
rate has no impact on them
 But Baumol showed that rate of interest also
affects Transaction motive for holding money.
-- Holding cash in hand gives high liquidity.
– But there is loss of interest as the money is
not deposited in a bank.
 Therefore rate of interest also affects
Transaction Demand for Money.
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3.
The Baumol Model
 Baumol model describes money
demand in terms of a trade off between
liquidity and rate of return.
 Assume that consumer can keep his
income in the form of either cash in
hand or in savings account deposits.
 Cash pays no nominal interest.
 The savings account pays interest rate
i, this is the opportunity cost of holding
cash.
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4.
Consumer’s choice
 The consumer has to decide between
keeping cash (liquidity) but no interest,
 and putting it in a saving deposit – earns
interest but less liquid.
 If he keeps in savings deposit, he has to
spend time and money to go to the bank to
withdraw cash.
 This is the opportunity cost of keeping money
in the bank.
 The consumer has to decide on the optimum
allocation of his funds – between cash and
savings deposits.
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5.
 Cost of Money Management M:
M = cost of withdrawal (NF) + cost of interest
foregone due to holding cash (iM)
 Baumol’s Model:
PY = total nominal spending, done gradually over
the year
i = nominal interest rate on savings account
N = number of trips consumer makes to the bank
to withdraw money from savings account
F = cost of a trip to the bank (e.g., if a trip takes 15
minutes and consumer’s wage is Rs.120/hour,
then F = Rs.30)
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6.
 Average money holdings is a function of N or
number of trips to the bank.
 This has to be minimised.
 If N=1, then the consumer keeps all his
income in the form of cash.
 He spends it gradually throughout a given
time period, say a year or a month,
 His expenditure is constant over the time
period.
 The money or cash in hand falls at a
constant rate, till it becomes zero at the end
of the time period.
Cost of holding money
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7.
Baumol model: The demand for money
 Assume that
consumer
keeps all
income in the
form of cash.
 Then he only
goes once to
the bank to
withdraw
cash.
 In one year,
his average
money
holdings = Y/2
Y
Money
holdings
Time
1 year
N = 1
Average
= Y/ 2
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8.
By keeping all
Y as cash, he
loses interest.
Supposing he
keeps half his Y
in savings
account,
Then he has to
make 2 trips to
withdraw
money.
So on average
he has Y/4
cash in hand.
Y
Time11/2
N = 2
Y/ 2
Average
= Y/ 4
If N = 3, then 3 trips to the bank and average
cash holdings = Y/6 8

9.
The cost of holding money
 In general, average money holdings =
Y/2N
 Foregone interest = i (Y/2N )
 Cost of N trips to bank = FN
total cost =
Y
i F N
N
  
2
 Given Y, i, and F, consumer chooses N to
minimize total cost
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10.
N
Cost Foregone
interest =
iY/2N
Cost of trips
= FN
Total cost
Finding the cost-minimizing N
For any value of N, the height of the red line equals the height
of the blue line plus the height of the green line at that N.
Equilibrium is at X, with N* optimum number of trips.
N*
X
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11.
total cost =
Y
i F N
N
  
2
2
0
2
i Y
F
N
  
 Take the derivative of total cost with
respect to N, set it equal to zero:
 Solve for the cost-minimizing N*
2
* i Y
N
F

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12.
The Money Demand Function
 The Baumol-Tobin money
demand function:
( ) = ( )
2
/ , ,d Y F
M P L i Y F
i

 Money demand depends positively
on Y or income and F or foregone
interest, and negatively on i.
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13.
Summary of Baumol’s model
– A transactions theory of money demand,
stresses “medium of exchange” function
– Real money demand (Md/P) depends
positively on spending (Y), negatively on the
nominal interest rate (i),
– Positively on the cost of converting
non-monetary assets to money (F)
– It forms the Micro foundation for the LM
curve model.
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